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Insurance Companies and Pension Plans Chapter 3 Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 1
Insurance Companies and Pension Plans
Chapter 3
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 1
Types of Life Insurance (pages 41-45)
Term life Whole life Variable life Universal life Endowment life Group life
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 2
Cost of Whole Life Insurance Compared with Annual Premium (Figure 3.1)
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015
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Cost per year
Annual PremiumSurplus
Investment of Surplus
Some contracts allow the policyholder to choose how the surplus is invested
There are tax deferral advantages compared with a regular investment and in some jurisdictions the beneficiary of a life insurance policy does not have to pay any tax
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 4
Annuity Contracts (pages 45-46)
Typically a lump sum payment is used to buy a life-time annuity
Annuity can start immediately or be deferred Accumulation value can depend in a
complicated way on the performance of stock indices
There may be penalty-free withdrawals
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 5
Extract from US Mortality Tables (2009): Male
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 6
Age Prob. death within one year
Prob. Survival Life expectancy (yrs)
30 0.001419 0.97372 47.52
31 0.001445 0.97234 46.59
32 0.001478 0.97093 45.65
33 0.001519 0.96950 44.72
Extract from US Mortality Tables (2009): Female
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 7
Age Prob. death within one year
Prob. Survival Life expectancy (yrs)
30 0.000662 0.98551 51.82
31 0.000699 0.98486 50.86
32 0.000739 0.98417 49.89
33 0.000780 0.98344 48.93
How Tables Are Used In Pricing Life Insurance
Consider a female aged 30 Probability of death during first year is 0.000662 Probability of death during second year is
(1-0.000662) × 0.000699
Probability of death during third year is(1-0.000662) × (1-0.000699) ×0.000739
etc Minimum premium is such that present value of inflows
equals present value of outflows.
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 8
Longevity Derivatives (page 50-51)
Used by life insurance companies and pension funds
A population is defined and coupon on a bond depends on the number of members of the population still alive
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 9
Property-Casualty Insurance
Property insurance is concerned with loss or damage to property from fire, theft, etc
Casualty insurance is concerned legal liability exposures
What are the biggest risks facing property-casualty insurers?
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 10
CAT Bonds (page 52)
CAT bonds are an alternative to traditional reinsurance
This is a bond issued by a subsidiary of an insurance company that pays a higher-than-normal interest rate.
If claims of a certain type are above a certain level, the interest and possibly the principal on the bond are used to meet claims
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 11
Example of Ratios for Property-Casualty Insurance (Table 3.2)
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Loss Ratio 75%
Expense ratio 30%
Combined ratio 105%
Dividends 1%
Combined ratio after dividends 106%
Investment income (9%)
Operating ratio 97%
When Do Premiums Change?
In life insurance premiums typically stay the same throughout the life of the contract
In property-casualty insurance premiums are changed from year to year as risks are reassessed
In heath insurance premiums can rise because of the overall cost of health care but not because the health risks of the policyholder increase
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 13
Moral Hazard and Adverse Selection (pages 55-56)
Moral hazard is the risk that the existence of the insurance policy causes the policyholder to take more risks
Adverse selection is the tendency for an insurance company to attract bad risks when it cannot perfectly distinguish between good and bad risks
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 14
Typical Summary Balance Sheet: Life Insurance (Investments are mostly long-term corporate bonds)
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 15
Assets Liabs and Net worth
Investments 90 Policy Reserves 80
Other assets 10 Sub Long Term Debt 10
Equity Capital 10
Total 100 100
Typical Summary Balance Sheet: Property-Casualty Insurance (Investments are mostly liquid shorter maturity bonds)
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 16
Assets Liabs and Net worth
Investments 90 Policy Reserves 45
Other assets 10 Unearned premiums 15
Sub Long Term Debt 10
Equity Capital 30
Total 100 100
Regulation of Insurance Companies
US: Mostly at the state level Europe: Mostly at the EU level
Risk Management and Financial Institutions 4e, Chapter 3, Copyright © John C. Hull 2015 17
Pension Plans Defined benefit plan
Contributions are pooled Benefits are determined by a formula dependent on the final
salary of the employee and the number of years of service
Defined contribution plan Contributions for each employee are kept separate and
invested on behalf of the employee When the employee retires the accumulated value of the
contributions is usually converted to an annuity
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Defined Benefit Plans
Actuaries estimate liabilities and calculate a surplus or deficit for the plan.
The discount rate used for private plans is the AA borrowing rate
Deficits must be funded by the company within a prescribed period
A perfect storm: Declining equity prices coupled with declining interest rates
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Are Defined Benefit Plans Viable?
Employer plus employee contributions are typically 15% of salary or less
Actuarial estimates show that about 25% of salary is necessary to fund most plans
Funds typically invest 60% in equities and are relying on good investment returns from equity investments to meet obligations
Should members of DB plans bear some of the risk associated with equity returns?
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